Let `f : A -> B`, and let `I_A` and `I_B` be identity functions on A and B respectively. Prove that `(f o I_A) = f` and `(I_B o f) = f`

Let f:A rarr B, and let I_(A) and I_(B) be identity functions on A and B respectively.Prove that (foI_(A))=f and (I_(B)Of)=f

If f:A to B is a function and I_(A), I_(B) are identify functions on A,B respectively then prove that foI_(A) = f = I_(B) of

If f : A rarr B be any function and if I_A : A rarr A, I_B : B rarr B be the identity functions, show that fo*I_A=f,I_Bof=f .

Let A = (a,b,c) and B = (p,q,r) and a function f : A rarrB be given by f = ((a,q), b,r), (c,p)) Is f invertible ? If so, find f^-1 and verify that f^-1 of = I_A and f of^-1 = I_B where I_A and I_B are identity fucnctions on A and B respectively.

From a point O in the interior of a A B C , perpendiculars O D ,\ O E and O F are drawn to the sides B C ,\ C A and A B respectively. Prove that: (i) A F^2+B D^2+C E^2=O A^2+O B^2+O C^2-O D^2-O E^2-O F^2 (ii) A F^2+B D^2+C E^2=A E^2+C D^2+B F^2